Analytic-Splatting: Anti-Aliased 3D Gaussian Splatting via Analytic Integration (2403.11056v2)

Abstract: The 3D Gaussian Splatting (3DGS) gained its popularity recently by combining the advantages of both primitive-based and volumetric 3D representations, resulting in improved quality and efficiency for 3D scene rendering. However, 3DGS is not alias-free, and its rendering at varying resolutions could produce severe blurring or jaggies. This is because 3DGS treats each pixel as an isolated, single point rather than as an area, causing insensitivity to changes in the footprints of pixels. Consequently, this discrete sampling scheme inevitably results in aliasing, owing to the restricted sampling bandwidth. In this paper, we derive an analytical solution to address this issue. More specifically, we use a conditioned logistic function as the analytic approximation of the cumulative distribution function (CDF) in a one-dimensional Gaussian signal and calculate the Gaussian integral by subtracting the CDFs. We then introduce this approximation in the two-dimensional pixel shading, and present Analytic-Splatting, which analytically approximates the Gaussian integral within the 2D-pixel window area to better capture the intensity response of each pixel. Moreover, we use the approximated response of the pixel window integral area to participate in the transmittance calculation of volume rendering, making Analytic-Splatting sensitive to the changes in pixel footprint at different resolutions. Experiments on various datasets validate that our approach has better anti-aliasing capability that gives more details and better fidelity.

Analytic-Splatting for Anti-Aliased 3D Gaussian Splatting

Introduction

Recent advancements in novel view synthesis, particularly those leveraging Neural Radiance Fields (NeRF), have underscored the importance of efficient and high-quality rendering techniques. Among these, 3D Gaussian Splatting (3DGS) emerges as a promising approach, offering a GPU-friendly rasterization pipeline for real-time rendering. Despite its advantages, 3DGS suffers from aliasing issues at varying resolutions, mainly due to its discrete sampling scheme that fails to account for pixel area in the shading process. This paper introduces Analytic-Splatting, a method that extends 3DGS by analytically approximating pixel area integration, thereby achieving superior anti-aliasing performance and detail fidelity.

Related Works

The paper situates its contributions within the broader context of neural rendering and anti-aliasing techniques. Notably, it discusses how traditional approaches to addressing the aliasing in neural volumetric representations, such as MipNeRF and Mip-Splatting, either compromise on detail preservation or introduce computational inefficiencies. Analytic-Splatting is positioned as a solution that neither suppresses high-frequency components nor requires excessive computational resources, thus preserving the quality of details in the rendered views.

Analytic-Splatting

The core innovation of Analytic-Splatting lies in its analytical approximation of the Gaussian signal's integral over pixel window areas. This method revisits the signal window response problem in 3DGS and proposes a conditioned logistic function as the analytical approximation for the cumulative distribution function (CDF) of one-dimensional Gaussian signals. This approximation facilitates the calculation of the Gaussian integral by subtracting the CDF values, effectively capturing the intensity response of each pixel across different resolutions. Analytic-Splatting then extends this approximation to two dimensions, leveraging the independence of Gaussian signals along the eigenvectors of their covariance matrix. This approach not only mitigates aliasing but also enhances the rendering fidelity.

Experiments

Empirical validation on various datasets demonstrates the superiority of Analytic-Splatting over existing methods, including 3DGS and Mip-Splatting, across multiple metrics (PSNR, SSIM, LPIPS). The method shows significant improvements in anti-aliasing capability and detail preservation, especially under multi-scale rendering conditions. The experiments underline the method's robustness and its ability to handle high-frequency details more adeptly than its predecessors.

Implications and Future Work

Analytic-Splatting presents a significant step forward in the quest for high-fidelity, real-time novel view synthesis. By addressing aliasing at its core, the method ensures that high-quality details are not lost in the rendering process, a critical concern for applications in virtual reality, augmented reality, and visual effects. The introduction of an analytical approximation for pixel area integration opens new avenues for research, potentially inspiring future work in efficient anti-aliasing techniques and neural rendering technologies.

In conclusion, Analytic-Splatting advances the capabilities of 3D Gaussian Splatting through an analytical approach to pixel shading, achieving both anti-aliasing and detail preservation. Its strong numerical results and the ability to maintain high-quality details at different resolutions position it as a valuable contribution to the field of neural rendering and 3D scene reconstruction.